Mean-Variance Utility


I would like to integrate Mean-Variance utility type trades in a Macro Model. These agents will typically hold a trading position

K = c0 * ER / VR

Where c0 is a parameter, ER is the expected return, VR is the variance.

What happens in steady state is ER=VR=0 and the traders are indifferent to hold any position. Lets say I want them to hold K*

However, the equation I listed becomes

K* = c0 * 0/0

Is there any way to get around this?


It seems your problem is to solve a portfolio problem. That will create issues when using perturbation around a deterministic steady state as you indicate. You could reformulate your equation by multiplying with VR, but that would still not solve the singularity in steady state. You might want to check out the work by Devereux/Sutherland.